Konan is the paper godddess. I find it funny and ironic that her paper overwhelmed jiraiya's katon, that anime logic though. Anyways, I think honestly this is just a battle of stamina. In the little skirmish during the pain arc, it was shown the bugs can eat away at her paper, and he can likely get bugs in the paper she uses to regenerate. Since konan can't keep up her immortality forever and the bugs will keep draining her chakra, she is likely to lose if she can't end shino quickly. So far my bet is on shino.
I never really saw Shino as being that strong. Konan on the otherhand was the first person to bring Tobi so far during a fight. Yeah he got hit during his fight with Minato, but that was 1. 16 years before current Tobi and 2. against Minato, one of the top tier characters in the series.
In any case, I think Konan has this. Shino doesn't really have the defense to face multiple barrages of paper bombs, and I think the only time we saw her going "all out" was during her battle with Tobi. Which was a pretty great display of her abilities.
I don't think she gave much care at all during the Konoha raid. I think her main goal was to keep some of the Leaf's fighters off of the paths, or as a distraction or whatever. It'd make more sense to think that she was conserving her energy to protect Nagato if the fight ever came to that.
The bugs will eat the paper and the chakra from them to prevent them from exploding.
Yet the paper clones still exploded when the bugs were on them. So they weren't quick enough to absorb the chakra.
As for the winner. The fact that Konan mixes explsive tags in with her paper and Shino has no x-ray vision or anything, it will be more dangerous for Shino as his bugs will continously blow up. Since it's clear Konan has way more chakra than Shino, she'd outlast him. She wins with mid difficulty.
Konan wins for sure now imo, I said draw beforehand before even thinking of the one thing that would proabably give her the win for sure if she fought Shino. Her effort and style of attack against Tobi was something to be intrigued by, and up until that point in the series, we had not seen anyone come remotely close to pushing Tobi as far as Konan did, going so far as to almost breaking Tobi's mask and revealing who he truly was. Shino would be overwhelmed by the quantity of paper bombs thrown at him and the angles of which they can come from, his bugs (as mentioned above in previous comments) would not have enough time to absorb chakra, therefore giving Konan a much better advantage in the fight, as Shino would only be able to rely on his bugs absorbing the chakra to trouble Konan. So yeah, Konan for the W.
That would be episode 162, however, Shibi and Mota are with Shino, so its 3v1 scenario when they take Konan on, but even still, it didn't seem like they were able to do anything really to affect her in any way, not that I can remember anyway.